The nation's top think tanks are reeling in more billionaire backers than ever before, and this trend underscores how the wealthy see these institutions as key players in shaping public policy.

Nowadays, if you really want to buy influence, you make political donations for sure, but you may give even more money to think tanks, which excel at framing the terms of public debates and putting specific ideas on the national agenda (or knocking other ideas off).

The think tank was invented in the mid-20th century to offer objective analysis of complex issues. Now, though, think tanks often operate as the motherships of ideological movements—weaving together a jumble of values and ideas into a coherent story and actionable agenda.

The wealthy have long backed think tanks, especially on the right. More recently, the founding of the liberal Center for American Progress was bankrolled by a billionaire couple, Herb and Marion Sandler.

Today, the most popular think tank among the ultra rich is the American Enterprise Institute. Why is that? And which billionaires, exactly, are backing this place?

One way to understand AEI's ties with the wealthy is that it's the smart conservative think tank in Washington.

If you're a rich right-winger who made your fortune opening car dealerships in the Sun Belt, you give to the Heritage Foundation, with it's Tea Party leader Jim DeMint and simple black-and-white view of how the world should work (in your favor).

If you're a wealthy libertarian, with the ideological sophistication of a 15-year-old boy ("Leave me alone!") you give your money to Cato.

But if you have a Wharton MBA and got wealthy with algorithm-based trading strategies, than AEI is your place, with its brainy president, Arthur Brooks, and a building stocked with Ph.D.s.

Back in the 1980s, many of America's wealthy had made their money in industry or real estate or retail. A shift toward a knowledge economy has produced an explosion of billionaires who got rich in finance or tech by monetizing their intelligence and Ivy League credentials. That change in how wealth is created helps explain why AEI is doing so well these days.

Heritage and AEI push many of the same positions—e.g., keep taxes on rich people low and make poor people get off their asses—but AEI does so in a more nuanced, sophisticated way. You won't find any Tea Party types floating around the building. (Although you might run into Dick Cheney in the elevator.)

Also, AEI doesn't just have a big brain, it has the stirrings of a heart. Arthur Brooks gets that the right seems oblivious to poverty, wage stagnation, and inequality, and he's been pushing for the institute to come up with conservative-friendly ways to address these problems.

Last year, Brooks even brought in the Dalai Lama for a chat. More importantly, he's made AEI a hot spot for younger intellectuals on the right, including some of the contributors to a recent volume of essays that offers up a less Darwinian conservative policy agenda.

Of course, all this plays well in the more cosmopolitan reaches of the upper class, where the rich will fight to the death to protect preferential tax treatment of capital gains, but often are worried about the millions of Americans being left behind these days. (Which is why a lot of them shower the Robin Hood Foundation with money and bankroll charter schools for low-income minority students.) Add to this the fact that Arthur Brooks actually enjoys fundraising, and surely hobnobs well at the Four Seasons (whereas DeMint would do better at a Dallas country club), and you can see why the big bucks have been rolling in.

That said, AEI also has plenty of more traditional conservative rich guys in its corner—including heartland industrialists and corporate CEOs. Some of these people also give money to other think tanks, too, including Heritage, Cato, and the Manhattan Institute. But the smart money has been flowing to AEI, both literally and metaphorically.

Just take a look at the list of AEI's billionaire supporters:

Philip Anschutz. The Colorado business magnate might seem more like a Heritage guy, with his Christian faith, but his biggest think tank donations go to AEI.

Daniel A. D'Aniello. The cofounder and chair of the Carlyle Group, serves as vice chair of AEI's board, and recently pledged $20 million for a new AEI building.

Richard DeVos. The Amway cofounder has given generously to AEI through his family foundation. Also gives to Heritage.

Seth Klarman. One of a number of ultra rich finance guys who sits on AEI's board.

Charles Koch. The industrialist mega billionaire is a big backer of Cato and gives to Heritage, but has also steadily channeled funds to AEI.

Bruce Kovner. New York hedge funder sits on AEI's board, and once was it's chair. Interestingly, Kovner is said not to consider himself a "conservative."

Peter Peterson. He's not a regular AEI supporter, since he has other think tanks to feed (with his name on them), but he did give $200,000 in 2011.

George Roberts. Cofounder of private equity firm KKR is a major donor to AEI.

Paul Singer. New York hedge funder backs other think tanks, particularly the Manhattan Institute, but clearly has a thing for AEI judging by over a million dollars in gifts in recent years.

Did I forget anyone? Probably so. In any case, these billionaires are just the tip of the AEI funding juggernaut. The think tank has also pulled in huge support from corporations, particularly ExxonMobil, and a host of wealthy donors who aren't billionaires, but awfully close.